By Gilbert Strang
This textbook is a well-organized treatise on calculus. the writer intuitively offers precise and in depth factors gratifying beginner’s wishes. The booklet is either invaluable as a reference and a self-taught guide of calculus. bankruptcy 1: creation to Calculus; bankruptcy 2: Derivatives; bankruptcy three: purposes of the by-product; bankruptcy four: The Chain Rule; bankruptcy five: Integrals; bankruptcy 6: Exponentials and Logarithms; bankruptcy 7: innovations of Integration; bankruptcy eight: purposes of the necessary; bankruptcy nine: Polar Coordinates and complicated Numbers; bankruptcy 10: endless sequence; bankruptcy eleven: Vectors and Matrices; bankruptcy 12: movement alongside a Curve; bankruptcy thirteen: Partial Derivatives; bankruptcy 14: a number of Integrals; bankruptcy 15: Vector Calculus; bankruptcy sixteen: arithmetic after Calculus
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Example text
Our aim is to support, with examples and information, the effort to use computing to help learning. For calculus, the gveatest advantage of the computev is to o$er graphics. You see the function, not just the formula. As you watch, f ( x ) reaches a maximum or a minimum or zero. A separate graph shows its derivative. Those statements are not 100% true, as everybody learns right away-as soon as a few functions are typed in. But the power to see this subject is enormous, because it is adjustable.
What is their (shortest) period? 4 Show that cos 28 and cos28 have period n and draw them on the same graph. 5 At 8 = 3n/2 compute the six basic functions and check cos28 + sin28, sec20 - tan2 8, csc28 - cot28. , 7 The area of a circle is nr2. What is the area of the sector that has angle 8? It is a fraction of the whole area. 8 Find the distance from (1, 0) to (0, 1) along (a) a straight line (b) a quarter-circle (c) a semicircle centered at (3,i). 9 Find the distance d from (1,O) to a circle why 6d is less than 2n.
Choose the center point and press E N T E R. The new graph appears. Change those scaling factors with Z 0 0 M S e t F a c t o r s . Best of all, create your own viewing window. Press Z 0 0 M B o x . To draw the box, move the cursor to one corner. Press E N T E R and this point is a small square. The same keys move a second (blinking) square to the opposite corner-the box grows as you move. Press E N T E R, and the box is the new viewing window. The graphs show the same function with a change of scale.